Lemma 52.15.6. Let A be a Noetherian ring. Let f \in \mathfrak a be an element of an ideal of A. Let U = \mathop{\mathrm{Spec}}(A) \setminus V(\mathfrak a). Assume
A has a dualizing complex and is complete with respect to f,
for every prime \mathfrak p \subset A, f \not\in \mathfrak p and \mathfrak q \in V(\mathfrak p) \cap V(\mathfrak a) we have \text{depth}(A_\mathfrak p) + \dim ((A/\mathfrak p)_\mathfrak q) > 2.
Then the completion functor
is fully faithful on the full subcategory of finite locally free objects.
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